You just need to add the code generated for the twitter widget to a text widget in your theme.
Go to: Appearance and click Widgets
Select which sidebar, in the little drop down menu, you want to add the widget to, and click on Show.
Look down the list of available widgets for Text, and click Add, then click Edit on the newly added widget.
In the top box, add some sort of title -- Twitter Updates for instance.
Select and copy the code in the box on the twitter page, and paste that into the bottom box. You are going to need to adjust the width setting in that code to suit your sidebar. Look through the code until you see width="290"; change that to number to 170 or something.
Click Done at the bottom of the widget box.
Click Save Changes and that should be all done. Check to see that your new widget is appearing on the site.
Hope that helps.